Graph the equation y=-1/8x^2+x-4

Which equation is the inverse of y = 9x2 - 4?

m_a_m_a [10]

Answer:

The inverse will be:

$y' = \frac{\sqrt{x+4}}{3}$

Step-by-step explanation:

In order to find the inverse of the equation, we do a variable change, since we are finding the inverse, :

$f(x) = 9x^{2} - 4$

$y = 9x^{2} - 4$

$x = 9y' ^{2} - 4$

Now solve for y'.

First add 4 in both sides of the equation and change to the left y'.

$x + 4= 9y'^{2} - 4+4$

$9y'^{2}$ = x + 4

Second divide by 9

$9y'^{2}$ /9 = (x + 4)/9

$y'^{2}$ = (x + 4)/9

Now you will have to clear y, with the square root.

$[tex]y'^{\frac{2}{2}} = \sqrt{x + 4} / \sqrt{9}$ [/tex] =

Simplifying terms

$y' = \frac{\sqrt{x+4}}{3}$

$f^{-1}(x) = \frac{\sqrt{x+4}}{3}$

You can check the answer by doing the evaluation of the following equation:

(f o $f^{-1}$ ) (x)

substitute the equation for y' or inverse function $f^{-1}$

f( $\frac{\sqrt{x+4} }{3}$ )

Now substitue the value into f(x)

You will have

$= 9(\frac{\sqrt{x+4} }{3}} )^{2} - 4\\\\Solving\\\\9(\frac{{x+4} }{9}} ) - 4$

=x

5 0

3 years ago

A certain electronics manufacturer found that the average cost C to produce x DVD/Blu- ray players can be found using the equati

lilavasa [31]

Answer:

The minimum average cost is $2.80 when 163 players are built

Step-by-step explanation:

Average Cost Function

We'll assume the given function as the total cost to produce x players, and NOT the average cost since that is a different definition, as shown below.

The cost C to produce x DVD/Blu- ray players is given by the equation

$C=0.03x^2-7x+800$

The Average Cost function is defined as

$\displaystyle\bar C=\frac{C}{x}$

$\displaystyle\bar C=\frac{0.03x^2-7x+800}{x}$

$\displaystyle\bar C=0.03x-7+\frac{800}{x}$

To find the extreme value of the average cost, we must take the first derivative of the function

$\displaystyle\bar C'=0.03-\frac{800}{x^2}$

Equating to 0

$\displaystyle 0.03-\frac{800}{x^2}=0$

Solving for x

$\displaystyle x=\sqrt{\frac{800}{0.03}}$

$x=163$

The second derivative is

$\displaystyle\bar C''=\frac{1600}{x^3}$

For x=163 the second derivative is positive, thus x=163 is a minimum value. Let's compute the minimum average cost

$\displaystyle\bar C(163)=0.03\cdot 163-7+\frac{800}{163}$

$\displaystyle\bar C(163)=2.80$

The minimum average cost is $2.80

5 0

3 years ago

1) Is this graph a linear function? Explain.....2) Is this graph a linear function? Explain....

Sav [38]

9514 1404 393

Answer:

no
no

Step-by-step explanation:

If the graph is not a straight line, it is not a linear function. Neither graph 1 nor graph 2 is a straight line, so neither is a linear function.

__

Graph 2 is made of parts of two straight lines. It is not one straight line, so not a linear function. It is called "piecewise linear," which is different.

6 0

3 years ago

Sales tax is a function of the price of an item. The amount of sales tax is 0.08 times the price of the item. Use h to represent

Margaret [11]

Option C:

h(x) = 0.08x

Solution:

Given data:

Sales tax is a function of the price of an item.

Let h be the function.

Take x be the price of an item.

Amount of sales tax = 0.08 times price of the item

= 0.08 × x

Amount of sales tax = 0.08x

⇒ h(x) = 0.08x

Hence the function is h(x) = 0.08x.

Option C is the correct answer.

5 0

3 years ago

Help on this please

AveGali [126]

18 11 25 8 4 !!!!!!!!

5 0

4 years ago